The present invention relates to a manufacturing technique for producing a cover for a vehicle airbag. Generally, in an airbag unit mounted on a vehicle, there is provided an airbag cover for covering the vehicle airbag. The airbag cover has a tear line (a linear groove) on its inner wall surface. Upon collision of the vehicle, the airbag cover is torn open along this tear line, and allows the vehicle airbag cover to be deployed and inflated toward the outside of the airbag cover. As a technique for providing the tear line by post-processing, a technique using laser cutting is disclosed in PCT Japanese Translation Patent Publication No. 2001-502996 (incorporated herein by reference). This patent document sets forth the possibility of forming a tear line using laser cutting. However, when manufacturing this type of airbag cover, a technique effective in accurately machining a tear line with a desired shape in the airbag cover is needed.